1. Field of the Invention
This invention regards an arrangement to correct the linear and nonlinear transfer behavior of electro-acoustical transducers, consisting of an electro-acoustical transducer, a distortion-reduction network connected to its input terminals, and a support system to fit the distortion-reduction network to the transducer. The distortion-reduction network shows nonlinear transfer characteristics obtained from modelling the transducer and thus changes the electrical signal such that the nonlinear effects of the network compensate for the nonlinear behavior of connected transducer. The result is an overall system with reduced distortion and improved linear transfer behavior. A fitting technique and system is used to change the parameters of the electrical network automatically to fit the actual transfer characteristics of the distortion reduction system to the transducer. Several mechanisms, unique to each transducer, are responsible for generation of nonlinear distortion.
The primary nonlinear distortion of an electro-dynamic transducer (loudspeaker, head phone, microphone, technical actuators) is caused by displacement varying parameters. Transducers using wave guides (e.g. horns) show additional distortion based on nonlinear compression- and flow characteristics. Electro-static microphones (condenser type) exhibit nonlinear distortion due to varying electric charges on the plates.
Reducing nonlinear signal distortion improves subjective listening impression in electro-acoustical recording and reproduction of music and increases the linearity of the output. The fields of measurements and active noise reduction require highly linear transducers.
Additionally, in noise cancelling systems, non-compensated non-linear distortion reduces the effectiveness of the system. Improved transducer design can result in better linearity but at a higher cost and with reduced efficiency. By adding an electric compensation system, transducer distortion can effectively be reduced and the linear and nonlinear transfer response improved.
2. Description of Related Art
The UK patent 1,031,145 for electro-acoustical transducers suggests the use of negative feedback. This method requires an electrical, mechanical or acoustical signal derived from the transducer or the radiated sound. This signal is compared with the electrical input signal and the error signal is used for driving the transducer.
Using negative feedback has the advantage that it is not necessary to know the exact nature of the nonlinearity and that the system also functions when the nonlinearity changes. However, the necessary pick-up systems are expensive, sensitive and have certain transfer characteristics which have to be compensated for by an appropriate distortion-reduction network. The danger of possible clipping also requires a protection system. Hall, D. S., Design Considerations for an Accelerometer Based Loudspeaker Motional Feedback System, 87 Audio Eng. Soc. Cony., New York October 1989 (Preprint 2863). All these problems have prevented broad application of this method. Consequently, it is desirable to realize a nonlinear correction system without permanent signal feed back.
By modeling the nonlinear characteristics of the transducer, the nonlinear transfer function can be described. Using these characteristics, a filter with the inverse transfer function can be designed which will compensate for the nonlinear behavior of the transducer.
One way of modeling the nonlinear transfer behavior of a transducer is based on the functional series expansion (e.g. VOLTERRA-series expansion). This is the most powerful technique to describe the second- and third-order distortions of nearly linear systems at very low input signals. However, if the system nonlinearities cannot be described by the second- and third-order terms of the series, the transducer will deviate from the model resulting in poor distortion reduction. Moreover, to use a Volterra-series the input signal must be sufficiently small to guarantee the convergence of the series according to the criterion of Weierstrass.
This theory was first applied to transducers by Kaiser, A. J., Modeling of the Nonlinear Response of an Electrodynamic Loudspeaker by a Volterra Series Expansion, J. Audio Eng. Soc. 35 (1987) 6, S. 421. In the small-signal domain, a good agreement between measured and calculated distortion was found, but at a higher level of input power there were effects which could not be explained by the second- and third-order VOLTERRA-series expansions. Klippel, W., The Large-Signal Behavior of Electrodynamic Loudspeakers at Low Frequencies, 90 AES Convention Paris 1991, preprint 3049.
If the VOLTERRA-series expansion of an any causal, time invariant, nonlinear system is known, the corresponding compensation system can be derived. Schetzen, M., The Volterra and Wiener Theories of Non-Linear Systems (Wiley, New York, 1980). From the VOLTERRA-series expansions, Kaiser derives an "Arrangement for converting an electric signal into an acoustical signal or visa versa and a nonlinear network for use in the arrangement" as described in U.S. Pat. No. 4,709,391 to Kaiser. Kaiser's arrangement comprises at least two circuit branches in parallel. One circuit branch compensates for the first order or linear distortion while each other circuit branch compensates for a different higher order distortion. This arrangement has a parallel structure according to the series properties of the functional series expansion (e.g. VOLTERRA-series expansions). The individual branches represent linear, quadratic, cubic or higher-order nonlinear networks and compensate for the appropriate distortion systems in the transducer model. The output of each branch is then added together to produce the output signal. This concept does not consider the specific characteristics of the transducer and is limited to second- and third-order correction systems in practice.
At low input levels, this system adequately compensates for non-linearities however, at higher levels the transducer deviates from the ideal second- and third-order model resulting in increased distortion of the transfer signal. In theory, a Volterra series can compensate perfectly for the transducer distortion, however, perfect compensation requires an infinite number of terms and thus an infinite number of parallel circuit branches. Adding some higher order compensation elements can increase the system's usable dynamic range. However, because of the complexity of elements required for circuits representing orders higher than third, realization of a practical solution is highly complex.
Recognizing the impracticability of higher order terms, this invention uses a different approach. Instead of a generic solution, this invention models the non-linear distortion characteristics of the transducer. Once the characteristics of the distortion are identified, a system having opposite characteristics can be created and used to compensate for the distortion in the transducer. Rather than the imperfect distortion reduction accomplished by Kaiser, this system creates a filter representing, within the scope of accuracy of the measurement of the characteristic of the transducer, a perfect distortion reduction network for the particular transducer. Fitting a nonlinear-distortion reduction network to the acoustical transducer has not been discussed in any literature, and no methods, supporting systems or automated procedures have been developed.
The goal of this invention is to create a distortion-reduction network without permanent feedback, which allows complete, automated (self learning) compensation of nonlinear distortion at small and large signal amplitudes (the transducer's full dynamic range). Moreover, as a system based on modeling the characteristics of the transducer, this invention be realized with fewer elements and less complexity than a Volterra series correction system.